On Wednesday, Mayor Ed Lee, in a widely expected move, named Chu as the city's assessor to replace Phil Ting, who was elected to the state Assembly in November.

"It comes as no surprise, probably for all of you, that I've chosen Carmen," Lee said during a public announcement in his office, calling Chu fiscally "brilliant" and praising her work on the city's first two-year budget.

The mayor did not swear her in, though, and Chu will remain as District Four supervisor until Lee picks her replacement on the board. The mayor said he would decide by March 4 who that would be.

Chu's designation sets off a mini political cascade at City Hall, with attention shifting to who will be appointed to represent the district that includes the Sunset and Parkside neighborhoods at the Board of Supervisors.

It also sets the stage for November elections for both posts - unless a special election is set sooner - and for maneuvering by potential challengers.

Chu's elevation to the citywide office of assessor, which carries a bump in pay to $173,736 from her $105,723 annual salary as a district supervisor, was seen by many observers as a natural fit. The politically moderate Chu is a former chair of the board's budget committee.

"I think she will be phenomenal," Supervisor Scott Wiener said. "She is smart, methodical and solutions-oriented."

Lee joked that rating service Moody's just upgraded the city's bond rating because it had heard the rumor that Chu would be in charge of property taxes.

The assessor oversees valuations of real estate for property taxes, the largest slice of revenue for the city's general fund, making up about 40 percent of the income.

With a city budget of $6.83 billion for the 2012-13 fiscal year, property tax and transfer tax revenue are projected to generate about $1.94 billion, with about $1.3 billion going to the city's general fund and the remainder split between the San Francisco Unified School District, San Francisco Community College District, BART and other entities, according to the assessor's annual report.

"All the things that we care about - being able to fund public services, police services, children's services, health services - these are all things that can only be accomplished when we have a very firm financial footing," Chu said.

As assessor, Chu would not face term limits, but she does have to try to hold her post in a November election to serve the remainder of Ting's term, which ends in January 2015. Her replacement would also face a November election to serve the remainder of Chu's supervisor term, also expiring in January 2015.

The selection is important for multiple reasons. Chu, representing a politically moderate district with a high number of homeowners and a sizable Chinese American population, has been a reliable vote for the mayor.

With the partial term, her replacement will have the opportunity to serve almost 10 years if he or she wins re-election, rather than the typical eight years.

Lee is also looking to avoid the blunder he made in his only other appointment to the Board of Supervisors: Christina Olague in January 2012.

Olague, a tenant activist and co-chair of the group behind the "Run, Ed, Run" campaign to persuade Lee to break his promise to serve as a one-year caretaker, comes from the city's political left.

She broke with Lee on several major votes, including her decision to reinstate Sheriff Ross Mirkarimi, whom the mayor charged with official misconduct after a domestic dispute with his wife.

Lee said he would take the time between now and March 4 to consult with District Four residents and review candidates.